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On the late‐time behavior of tracer test breakthrough curves

On the late‐time behavior of tracer test breakthrough curves We investigated the late‐time (asymptotic) behavior of tracer test breakthrough curves (BTCs) with rate‐limited mass transfer (e.g., in dual‐porosity or multiporosity systems) and found that the late‐time concentration c is given by the simple expression c = tad{c0g − (m0(∂g/∂t))}, for t ≫ tad and tα ≫ tad, where tad is the advection time, c0 is the initial concentration in the medium, m0 is the zeroth moment of the injection pulse, and tα is the mean residence time in the immobile domain (i.e., the characteristic mass transfer time). The function g is proportional to the residence time distribution in the immobile domain; we tabulate g for many geometries, including several distributed (multirate) models of mass transfer. Using this expression, we examine the behavior of late‐time concentration for a number of mass transfer models. One key result is that if rate‐limited mass transfer causes the BTC to behave as a power law at late time (i.e., C ∼ t−k), then the underlying density function of rate coefficients must also be a power law with the form αk−3 as a α → 0. This is true for both density functions of first‐order and diffusion rate coefficients. BTCs with k < 3 persisting to the end of the experiment indicate a mean residence time longer than the experiment, and possibly an infinite residence time, and also suggest an effective rate coefficient that is either undefined or changes as a function of observation time. We apply our analysis to breakthrough curves from single‐well injection‐withdrawal tests at the Waste Isolation Pilot Plant, New Mexico. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Water Resources Research Wiley

On the late‐time behavior of tracer test breakthrough curves

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References (60)

Publisher
Wiley
Copyright
Copyright © 2000 by the American Geophysical Union.
ISSN
0043-1397
eISSN
1944-7973
DOI
10.1029/2000WR900214
Publisher site
See Article on Publisher Site

Abstract

We investigated the late‐time (asymptotic) behavior of tracer test breakthrough curves (BTCs) with rate‐limited mass transfer (e.g., in dual‐porosity or multiporosity systems) and found that the late‐time concentration c is given by the simple expression c = tad{c0g − (m0(∂g/∂t))}, for t ≫ tad and tα ≫ tad, where tad is the advection time, c0 is the initial concentration in the medium, m0 is the zeroth moment of the injection pulse, and tα is the mean residence time in the immobile domain (i.e., the characteristic mass transfer time). The function g is proportional to the residence time distribution in the immobile domain; we tabulate g for many geometries, including several distributed (multirate) models of mass transfer. Using this expression, we examine the behavior of late‐time concentration for a number of mass transfer models. One key result is that if rate‐limited mass transfer causes the BTC to behave as a power law at late time (i.e., C ∼ t−k), then the underlying density function of rate coefficients must also be a power law with the form αk−3 as a α → 0. This is true for both density functions of first‐order and diffusion rate coefficients. BTCs with k < 3 persisting to the end of the experiment indicate a mean residence time longer than the experiment, and possibly an infinite residence time, and also suggest an effective rate coefficient that is either undefined or changes as a function of observation time. We apply our analysis to breakthrough curves from single‐well injection‐withdrawal tests at the Waste Isolation Pilot Plant, New Mexico.

Journal

Water Resources Research – Wiley

Published: Dec 1, 2000

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